On $B_{s} \to \mu^{+} \mu^{-}$ and Cold Dark Matter Scattering in the MSSM with Non-Universal Higgs Masses

We show that present experimental constraints on B_s -> mu+ mu- decay and the CDMS upper limit on the cold dark matter elastic scattering cross section already have significant impact on the parameter space of the minimal supersymmetric extension of the Standard Model (MSSM) with non-universal supersymmetry-breaking scalar masses for the Higgs multiplets (NUHM). The relaxation of scalar universality in the MSSM allows the possibility of a relatively light mass M_A for the pseudoscalar Higgs boson. The present upper limit on B_s -> mu+ mu- already excludes much of the scope for this possibility in the NUHM, in contrast to the constrained MSSM with universal scalar masses (CMSSM), where B_s -> mu+ mu- decay does not exclude any ranges of parameters not already excluded by b -> s \gamma decay. Cold dark matter scattering is also enhanced for small M_A, but the impact of present upper limit on B_s -> mu+ mu- on the NUHM parameter space is in many cases greater than that of the CDMS scattering limit, particularly at large tanb.